64 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013
Damping of SSR Using SubsynchronousCurrent Suppressor With SSSC
R. Thirumalaivasan, Member, IEEE, M. Janaki, Member, IEEE, and Nagesh Prabhu, Member, IEEE
Abstract—Hybrid series compensation using static synchronousseries compensator (SSSC) and passive series capacitor can im-prove the stability of the system, increases the power transfercapability and is useful for the fast control of power flow. Thispaper analyzes the subsynchronous resonance (SSR) character-istics of the hybrid series compensated power system in detailand proposes a simple method for the extraction of subsyn-chronous components of line current using filter. The extractedsubsynchronous frequency component of line current is used toinject a proportional subsynchronous voltage in series with thetransmission line which suppresses subsynchronous current inthe transmission network. This novel technique is termed as sub-synchronous current suppressor. The design of subsynchronouscurrent suppressor is based on damping torque analysis and usinggenetic algorithm. A novel graphical representation of seriesresonance condition when SSSC is incorporated in the systemis presented. The detailed study of SSR is carried out based oneigenvalue analysis, transient simulation and damping torqueanalysis. The results of the case study on a system adapted fromIEEE First Benchmark Model demonstrates the effectiveness androbust performance of subsynchronous current suppressor indamping of SSR under various system operating conditions.Linear analysis is performed on D-Q model of the system with
SSSC and the results are tested by executing transient simulationbased on detailed nonlinear three-phase model.
S ERIES compensation is an economic solution to improvethe stability of transmission system and increases the
power transfer capability. However, the potential inherentproblem in series compensated transmission lines connected toturbo generators is subsynchronous resonance (SSR) leadingto adverse torsional interactions [1]–[4] which results in shaftfailure of mechanical system.The onset of series connected FACTS controllers, like
thyristor controlled series capacitor (TCSC) and static Syn-chronous series compensator (SSSC), has made it possible notonly to regulate power flow in critical lines and also to counterthe problem of SSR. SSSC has several advantages over TCSC.
Manuscript received March 20, 2011; revised August 27, 2011, December22, 2011, and February 09, 2012; accepted March 23, 2012. Date of publicationMay 30, 2012; date of current version January 17, 2013. Paper no. TPWRS-00242-2011.R. Thirumalaivasan and M. Janaki are with the School of Electrical Engi-
neering, VIT University, Vellore-632014, India.N. Prabhu is with Canara Engineering College, Benjanapadavu, Bantwal,
Mangalore-574219, India (e-mail: [email protected]).Digital Object Identifier 10.1109/TPWRS.2012.2193905
SSSC is a voltage source converter (VSC) based FACTS con-troller, and has one degree of freedom (i.e., reactive voltagecontrol) injects controllable reactive voltage in quadrature withthe line current. The risk of SSR can be minimized by a suit-able combination of hybrid series compensation consisting ofpassive components and VSC based FACTS controllers suchas STATCOM or SSSC. The advantage of hybrid compensa-tion is reported in [5] and shown that reactive voltage controlmode of SSSC reduces the potential risk of SSR by detuningthe network resonance. The SSR characteristics of TCSC andSSSC are compared in [6] and studies indicate that vernier op-eration of TCSC is often adequate to damp SSR whereas a sub-synchronous damping controller (SSDC) with SSSC is desiredfor damping critical torsional modes when the line resistance islow. A method for online estimation of subsynchronous voltagecomponents in power systems is described in [7] and used forthe mitigation of SSR [8]. The damping of SSR using singlephase VSC based SSSC is reported in [9].In this paper, the analysis and simulation of a hybrid series
compensated system with SSSC based on three-level 24-pulse[10] VSC is presented. Themajor objective is to investigate SSRcharacteristics of the hybrid series compensated power systemin detail using both linear analysis, nonlinear transient simula-tion and propose a simple method for the extraction of subsyn-chronous component of line current using filter. The extractedsubsynchronous frequency component of line current is used toinject a proportional subsynchronous voltage in series with thetransmission line which suppresses subsynchronous current inthe transmission network. This novel technique is termed as sub-synchronous current suppressor and effectively mitigates SSR.The study system is adapted from IEEE FBM and the anal-
ysis is executed based on damping torque analysis, eigenvalueanalysis, and transient simulation. The paper is organized as fol-lows: In Section II, modeling of SSSC and the different methodsof analysis of SSR are given. Section III gives a case study andhighlights the importance of filters to damp SSR under varyingsystem parameters. Performance evaluation and the design ofsubsynchronous current suppressor is given in Section IV. Con-clusions drawn based on case studies are given in Section V.
II. MODELING OF SSSC AND ANALYSIS OF SSR
The converter circuit of SSSC is usually a multi-pulse and/ormultilevel configuration. In this work, SSSC is modeled bya combination of three-level, 24-pulse configuration withTYPE-1 controllers [11]. In three-level converter topology themagnitude of converter output voltage is controlled by varyingdead angle with fundamental switching frequency [5], [12],[13]. With the help of Type-1 controller, both the magnitude
THIRUMALAIVASAN et al.: DAMPING OF SSR USING SUBSYNCHRONOUS CURRENT SUPPRESSOR WITH SSSC 65
Fig. 1. Switching function for a three-level converter.
and phase angle of converter output voltage can be controlledand the converter pole voltage is zero for the time durationof per cycle. The harmonic distortion on the ac side isgreatly reduced by using three-level converter.In this paper, the detailed three-phase model of SSSC is de-
veloped by modelling the converter operation using switchingfunctions. The switching function for phase “a” is shownin Fig. 1.The switching functions of phase b and c are similar but phase
shifted successively by 120 in terms of the fundamental fre-quency. Assuming that the dc capacitor voltages
, the converter terminal voltages with respect to the midpoint of dc side “N” can be obtained as
(1)
and the converter output voltages with respect to the neutral oftransformer can be expressed as
(2)
whereis the switching function for phase “a” of a six-pulse three-levelVSC. Similarly for phase “b”, and for phase “c”, canbe derived. The peak value of the fundamental and harmonicsin the phase voltage are found by applying Fourier analysison the phase voltage and can be expressed as
(3)
where , 5, 7, 11, 13 and is the dead angle (period)during which the converter pole output voltage is zero. We caneliminate the 5th and 7th harmonics by using a twelve-pulseVSC, which combines the output of two six-pulse convertersusing transformers.The switching functions for first twelve-pulse converter are
given by
where
(4)
The switching functions for second twelve-pulse converter aregiven by
where
(5)
The switching functions for a 24-pulse converter are given by
(6)
The two 12-pulse converters are interfaced to obtain three-level24-pulse VSC based SSSC. The converter output voltage aregiven by
(7)
where .If the switching functions are approximated by their funda-
mental components (neglecting harmonics) for a 24-pulse three-level converter, we get
(8)
and , are phase shifted successively by 120 .The line current is given by
and are phase shifted successively by 120 . Note thatis the angle by which the fundamental component of converteroutput voltage leads the line current. It should be noted that isnearly equal to depending upon whether SSSC injects
66 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013
Fig. 2. Switching function of 24-pulse three-level converter analogous to a48-pulse converter when .
Fig. 3. Schematic representation of SSSC.
inductive or capacitive voltage. Neglecting converter losses wecan get the expression for dc capacitor current as
(9)
A particular harmonic reaches zero, when .At , the switching function for phase “a” isshown in Fig. 2 and indicates that 24-pulse three-level converterbehaves like a 48-pulse converter when as 23rd and25th harmonics are negligibly small.
A. Mathematical Model of SSSC in D-Q Frame of Reference
When switching functions are approximated by their funda-mental frequency components, neglecting harmonics, SSSC canbe modeled by transforming the three-phase voltages and cur-rents to D-Q variables using Kron’s transformation [15]. TheSSSC can be represented functionally as shown in Fig. 3.In Fig. 3, and are the resistance and reactance of the
interfacing transformer of VSC. The magnitude control of con-verter output voltage is achieved by modulating the conduc-tion period affected by dead angle of a converter while the dcvoltage is maintained constant.The converter output voltage can be represented in the D-Q
frame of reference as
(10)
where and are the D and Q components of SSSC injectedvoltage and are defined as follows:
(11)
(12)
Fig. 4. Phasor diagram of SSSC.
where is the modulation index [5]. For a 24-pulse three-levelconverter the modulation index is a function of dead angle andis given by . is the transformation ratio of SSSCinterfacing transformer. From the control point of view it is con-venient to define the real voltage and reactive voltagewhich are the components of in phase and quadrature withline current , respectively, and the phasor diagram is shown inFig. 4. and in terms of variables in D-Q frame ( and) are obtained as
(13)
(14)
Here, positive indicates inductive mode of operation ofSSSC and positive indicates that SSSC absorbs active powerfrom the line.The dc side capacitor is described by the dynamical equation
as
(15)
where ,, ( —base frequency), —susceptance of dc side capac-
itor, —conductance which accounts for losses.and are the D-Q components of the line current .
is the phase angle of line current and is the angle by whichconverter output voltage leads the line current.
B. SSSC Voltage Control (Three-Level VSC)
In Type-1 controller both magnitude (modulation index )and phase angle of converter output voltage are controlled.The dc side capacitor voltage is maintained at a constantvoltage by controlling real voltage . The real voltage refer-ence is obtained as the output of dc voltage controller.The reactive voltage reference may be kept constant
or obtained from a power scheduling controller. However, forthe SSR analysis constant reactive voltage control is considered.
THIRUMALAIVASAN et al.: DAMPING OF SSR USING SUBSYNCHRONOUS CURRENT SUPPRESSOR WITH SSSC 67
Fig. 5. Type-1 controller for SSSC.
It should be noted that harmonic content of the SSSC injectedvoltage would vary depending upon the operating point sincemagnitude control will also govern the switching.The dc capacitor voltage reference can be varied (depending
on reactive voltage reference) so as to give optimum harmonicperformance. In three-level 24-pulse converter, dc voltage ref-erence may be adjusted by a slow controller to get optimum har-monic performance at in steady state.The structure of type-1 controller for SSSC is given in Fig. 5.
In this figure, and are calculated as
(16)
(17)
C. Analysis of Subsynchronous Resonance
The SSR is analyzed based on damping torque, eigenvalueanalysis and transient simulation [14]. The steady-state SSR isanalyzed based on damping torque and eigenvalue analysis withlinearized models at the operating point. The transient SSR isanalyzed by transient simulation with nonlinear model of thesystem, where the generator stator transients are taken into ac-count with the detailed generator model (2.2) [15]. The trans-mission line is modeled by lumped resistance and inductance toconsider the effect of line transients.The graphical representation of resonance condition using
impedance function of SSSC on single phase basis is presentedin this paper in Section III and is a novel representation to val-idate the results of damping torque and eigenvalue analysis. Itshows the variation of inductive and capacitive reactances withfrequency varied from 10–300 rad/s. This graphical represen-tation presents a clear picture of possible SSR condition in thesystem.
III. CASE STUDY
The system under study is adapted from IEEE FBM [16]which consists of a turbine, generator (2.2 model), series com-pensated long transmission line and SSSC injecting a seriesvoltage in the transmission line is shown in Fig. 6.The analysis is carried out by considering the following as-
sumptions and initial operating condition.
Fig. 6. Modified IEEE First Benchmark Model with SSSC.
1) The generator supplies power of 0.9 p.u. to the trans-mission line.
2) The mechanical input power to the turbine is made con-stant.
3) The total series compensation is kept at 0.76 p.u. The studyis carried out for the following casesCase-1:Without SSSCCase-2:With SSSC In Case-1, Fixedcapacitor alone is used for the series compensation with
and in Case-2, hybrid compensa-tion is used wherein 0.25 p.u. of series compensation is metby SSSC and the remaining compensa-tion is provided by fixed capacitor .
4) In transient simulation, a small mechanical disturbance of10% step decrease in mechanical input torque is applied at0.5 s and restored at 1 s1 s is considered. To validate theeffectiveness of SSSC under severe fault, a three-phase toground fault applied at generator terminal at 1 s and clearedafter three cycles is considered.
A. Eigenvalue Analysis
The eigenvalues of the system matrix for the linearizedsystem about an operating point are given in Table I for case1 and case 2. It should be noted that, without SSSC, i.e.,in case-1, mode-1 becomes unstable at the operating pointconsidered. It is to be noted that with the inclusion of SSSC,(case-2) undamping of mode-1 is reduced and the frequency ofnetwork mode (sub) is increased to 128.4 rad/s. This networkmode closely matches with torsional mode-2 and it turns outto be unstable. This indicates that the introduction of SSSC forseries compensation increases and shifts the network resonantfrequency.
B. Transient Simulation
The transient simulation is carried out for the combined non-linear system which includes SSSC represented by both D-Qand three-phase model using MATLAB-SIMULINK [17].The transient simulation results for a step change of 10% de-
crease in the mechanical input torque applied at 0.5 s and re-stored at 1 s with three-phase model of three-level VSC based
68 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013
TABLE IEIGENVALUES OF THE COMBINED SYSTEM WITH AND WITHOUT SSSC
Fig. 7. Variation of rotor angle and LPA-LPB section torque for step changein input mechanical torque with three-phase model of three-level VSC basedSSSC.
SSSC is shown in Fig. 7. It is clear from Fig. 7 that the systemis unstable as the LPA-LPB section torque grows with time.
C. Discussion
The SSR problems under various operating conditions canbe predicted by using damping torque analysis. The correla-tion of damping torque analysis and eigenvalue results in pre-dicting torsional mode stability is discussed in detail in [18]which demonstrates the importance of damping torque analysisto determine the torsional mode stability.1) Damping Torque Analysis With Linearized Model of
SSSC: Variation of damping torque is shown in Fig. 8 for case1 and 2. It is to be noted that without SSSC (case-1), dampingtorque goes maximum negative at a frequency of about 98rad/s and matches with torsional mode-1 frequency and severetorsional interactions are expected. In case-2 with the inclusion
Fig. 8. Variation of damping torque with and without SSSC.
of SSSC, the peak negative damping is significantly reducedand shifts the network mode frequency (subsynchronous) andhence undamping of torsional mode-1 is also reduced. Theshifted subsynchronous electrical frequency matches withmode-2 torsional frequency (127 rad/s) and the correspondingtorsional mode becomes unstable. These results are consistentwith eigenvalue analysis.2) Graphical Representation of Resonance Condition: The
representation of impedance function of SSSC in single phasebasis from that of D-Q axis is given below.To obtain , the SSSC equations (along with controller) arelinearized at the operating point and expressed as
(18)
(19)
(20)
where
is identity matrix.
(21)
The resistance and the emulated reactance of SSSCon single phase basis as a function of frequency is computedfor case-2 with . It is found that, the resistance
THIRUMALAIVASAN et al.: DAMPING OF SSR USING SUBSYNCHRONOUS CURRENT SUPPRESSOR WITH SSSC 69
Fig. 9. Graphical representation of resonance conditions with and withoutSSSC.
is negligible while the emulated reactance ispractically constant with frequency as shown in Fig. 9.The graphical representation of resonance frequency is
shown in Fig. 9 for cases 1 and 2. It shows the variation ofinductive and capacitive reactances with frequency varied from10–300 rad/s. In case-1, when the fixed capacitor provides76% of compensation the resonance oc-curs at , where . In case-2,where compensation of 76% is met by and
, the effective capacitive reactanceis obtained by adding the constant reactance offered bySSSC to that offered by fixed capacitor . The variation ofeffective capacitive reactance with frequency isalso shown in Fig. 9. Now the resonance occurs at a frequencyof , where and this isconsistent with the subsynchronous network mode frequency
as obtained byeigenvalue analysis and about 127 rad/s obtained by dampingtorque analysis with SSSC.The effect of additional series compensation by SSSC to sup-
plement the existing fixed capacitor is to increase the elec-trical resonance frequency of the network. However, this in-crease in frequency is not significant as compared to that ob-tained with the equivalent fixed capacitor offering additionalcompensation (case-1, in this case). Thisillustrates that the SSSC is not strictly SSR neutral however, itoffers a reactance which remain practically constant with fre-quency.Hence it is obvious that, to mitigate SSR, the damping of crit-
ical torsional modes should be improved by reducing the neg-ative damping. This paper investigates the application of sub-synchronous current suppressor for damping SSR. The subsyn-chronous components of line current can be extracted from thenetwork using filters with narrow pass band. The extracted sub-synchronous line current components are used to inject propor-tional voltages by SSSC to suppress the subsynchronous cur-rents flowing in the generator. A systematic method to extract
subsynchronous frequency components using filters and miti-gation of SSR using subsynchronous current suppressor is pre-sented in the following section.
IV. DESIGN OF SUBSYNCHRONOUS CURRENT SUPPRESSOR
Damping of SSR can be obtained by designing a subsyn-chronous damping controller (SSDC) which provides positivedamping in the range of critical torsional mode of frequencies[14]. Damping of SSR using STATCOM is achieved by SSDCwhich takes Thevenin voltage signal (a synthesized voltage)[19] using locally available STATCOM bus voltage and isused to modulate the reactive reference current to improve thedamping of unstable torsional modes. The present work pro-poses the improvement of damping of critical torsional modesby extracting subsynchronous components of line current andinjecting a proportional voltage to suppress the subsynchronousfrequency currents. This is a simple method which reduces themagnitude of subsynchronous currents flowing through thegenerator and is termed as subsynchronous current suppressor(SSCS).The extraction of subsynchronous frequency current com-
ponent is achieved by band-pass filters operate in rotatingD-Q coordinates. Accordingly the tuning of filters depends onthe multimass turbine-generator shaft torsional frequencies.Hence it is adequate to design filter based on the knowledgeof torsional mode frequencies to extract the subsynchronousfrequency components to damp SSR. In this paper, the IEEEFBMwith six mass mechanical system is considered, which hasfive natural torsional mode frequencies [4]. The torsional modefrequency is taken as the center frequency and the pass band offilter is chosen from the eigen value analysis in which torsionalmode is unstable for the band of subsynchronous network modefrequencies closer to that of critical torsional frequency. Thefrequency response of band-pass filters for all critical torsionalmodes are shown in Fig. 10. This method of filter design isalso valid for any transmission network topologies as only thecomplement of network resonance frequenciesmatches with torsional frequencies cause SSR. Theblock diagram of subsynchronous current suppressor to extractsubsynchronous frequency components from the line current isshown in Fig. 11. Two band-pass filters (in D-Q frame) are usedto extract each torsional frequency component andfrom the line current and . Each filter set is effective onlyfor their corresponding torsional mode frequency and improvethe damping of respective torsional modes by reducing thenegative damping. Subsynchronous current suppressor extractssubsynchronous frequency currents corresponding to modes1, 2, 3, and 4 passed through appropriate gains to forobtaining and and sum up the signal to obtain
and as mentioned in the following:
where is the torsional mode ( , 2, 3, and 4).
70 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013
Fig. 10. Frequency response of band-pass filters.
Fig. 11. Block diagram of subsynchronous current suppressor.
Since modal inertia of torsional mode 5 is very high, mode 5is never excited and filter to extract mode 5 frequency compo-nent is not desired. The extracted subsynchronous voltage or-ders and (in D-Q frame of reference) are transformedto inphase and quadrature components and , re-spectively, and are used to modulate the in phase and quadraturevoltage orders and of SSSC as shown in Fig. 12.The subsynchronous frequency components of various
modes extracted from line current are passed through a suitablegains to and the damping of critical torsional modes areimproved by properly tuning to using GA making useof damping torque analysis. Genetic algorithm has been usedto optimize the parameters of control system that are complexand difficult to solve by conventional optimization methods[20]. In the following section optimization of subsynchronouscurrent suppressor parameters based on damping torque usingGA is presented.
Fig. 12. Type-1 controller for SSSC with extracted subsynchronous frequencycomponents from subsynchronous current suppressor.
A. Application of Genetic Algorithm for Optimization ofSubsynchronous Current Suppressor Parameters
The objective of subsynchronous current suppressor is to en-hance the damping torque by reducing the negative damping atcritical torsional mode frequencies. The synchronizing torque attorsional frequencies are not significantly affected by the elec-trical network (with or without damping controller [14]), henceit is simpler to design subsynchronous current suppressor by op-timizing the gains to with the objective to minimize thedeviations between the desired damping torque andactual damping torque to reduce the negative damping inthe range of all torsional mode frequencies. Genetic algorithmis adopted for optimizing the gains of subsynchronous currentsuppressor to ensure the stability in the complete range of allcritical torsional mode frequencies.On the basis of these facts, the objective function is defined
as
minimize (22)
where , is the p.u.deviation in generator rotor speed and is the p.u. changein electric torque, is the summation of squared error overthe range of series compensation ( to 0.75 p.u and
, and ) up to 100%. Toensure the stability of the system, the objective function is sub-jected to the constraint that
Real part of all eigenvalues (23)
In order that subsynchronous current suppressor minimizes thenegative damping, the desired damping torque is taken as pos-itive while ensuring all eigenvalues to have negative real parts.However, it was noticed that, when the value of islarge positive, network mode becomes unstable. Here, the de-sired damping torque is taken as 8 p.u. for the entirerange of torsional frequencies. The outcome of GA optimiza-tion is the gains to which remain unchanged at variousoperating conditions while ensuring system stability.
B. Analysis of SSR With Subsynchronous Current Suppressor
The analysis is performed based on eigenvalue analysis,damping torque analysis and transient simulation. D-Q modelof SSSC is considered for damping torque and eigenvalue
THIRUMALAIVASAN et al.: DAMPING OF SSR USING SUBSYNCHRONOUS CURRENT SUPPRESSOR WITH SSSC 71
Fig. 13. Damping torque with SSSC and SSCS.
analysis and the detailed three-phase model of SSSC is usedfor transient simulation.1) Damping Torque Analysis: The damping torque with
SSSC and GA optimized subsynchronous current suppressor(case-3) is shown in Fig. 13. It is to be noted that, the peaknegative damping is greatly reduced with subsynchronouscurrent suppressor.The negative damping is negligible in the range of torsional
frequencies (60–300 rad/s) and the system is expected to bestable with the intrinsic mechanical damping and the transmis-sion line resistance. The variation of real part of eigenvalue ofall torsional modes with compensation level is shown in Fig. 14when themechanical damping is neglected. Referring to Fig. 14,it is observed that all the torsional modes are stable with the pro-posed subsynchronous current suppressor using optimal param-eters when the hybrid compensation is varied from 0.3 p.u. to 1p.u. This demonstrates the robustness of the designed subsyn-chronous current suppressor in damping subsynchronous oscil-lations in the range of series compensation.The variation of total effective capacitive reactance incor-
porating subsynchronous current suppressor isshown in Fig. 15 (case-3), it is observed that is not constantwith frequency due to the presence of filters used in subsyn-chronous current suppressor. The total effective capacitive reac-tance incorporating subsynchronous current suppressor
never becomes equal to in the frequency range of50–275 rad/s. It is to be noted that between 275 to 300 rad/s, theeffective capacitive reactance is equal to at two frequencies,which are close to torsional mode-5. Since the modal inertia ofmode-5 is high, it is unaffected and remain stable as shown inFig. 14. All other torsional modes (1–4) and swing mode (0)are also found to be stable when hybrid compensation is variedfrom 0.3 p.u. to 1 p.u. This clearly indicates that the designedsubsynchronous current suppressor ensures that the series com-pensated power system is free from SSR.2) Eigenvalue Analysis: The eigenvalues of the system with
three-level VSC-based SSSC and SSCS are shown in Table II.Comparing the eigenvalue results of with SSSC and without
subsynchronous current suppressor (Table I, col-2) and with the
Fig. 14. Variation of real part of eigenvalue of torsional modes with compen-sation level with SSSC and SSCS.
Fig. 15. Variation of emulated reactance of SSSC with SSCS.
TABLE IIEIGENVALUES OF THE COMBINED SYSTEM WITH SSSC AND SSCS
presence of both SSSC and subsynchronous current suppressor(Table II), the following observations can be made.1) With subsynchronous current suppressor, the damping oftorsional modes 1 and 2 has significantly improved.
72 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013
2) The damping of torsional mode-3 and mode-4 is margin-ally increased with subsynchronous current suppressor.
3) Damping of mode-0 is marginally decreased.4) Modal inertia of Mode-5 is very high and hence is not ex-cited.
5) The damping of subsynchronous network mode is signifi-cantly increased with subsynchronous current suppressor.
3) Transient Simulation: The transient simulation has beencarried out for the overall system including SSSC with sub-synchronous current suppressor using MATLAB-SIMULINK[17]. Fig. 16 shows the simulation results for full load of
with the step change of 10% decrease in the input me-chanical torque applied at 0.5 s and removed at 1 s and sub-synchronous current suppressor is activated at . It is ob-served that the section torque is growing with time until ,when subsynchronous current suppressor is activated at ,the oscillations of shaft section torque decays with time. TheFFT analysis of the LPA-LPB section torque is performed be-tween 3–8 s with the time spread of 1 s and is shown in Fig. 17.Referring to Fig. 17, it is observed that in the time span of 3–5 s,the mode-1 component is predominant and increases with time.When SSCS is activated at 5 s, the mode-1 component decayswith time and demonstrates the effectiveness of subsynchronouscurrent suppressor to suppress the subsynchronous frequencycomponents in the line. Transient simulation for three-phasefault at generator terminal with fault impedance as given inIEEE FBM [16] is applied at 1 s cleared after three cycles with
and are shown in Figs. 18 and 19,respectively. The SSCS gain values to remain unchangedin all operating points and is observed that with SSCS the os-cillations of section torque decay with time. The line currentand D-Q components of subsynchronous current when
and following three-phase fault at generator terminalswith SSCS are shown in Fig. 20. It shows that SSCS extractssubsynchronous frequency components even when the funda-mental frequency line current is zero . It is to benoted that, under disturbance conditions the line is expected tocarry currents due to energy exchange between mechanical andelectrical system at their natural frequencies. As a result, thetransmission line carries both subsynchronous and supersyn-chronous frequency current components . The su-persynchronous frequency currents in the network contributespositive damping torque [4]. It is the subsynchronous frequencycomponent of network currents that cause negative damping.Under disturbances, torsional mode-1 (98 rad/s) gets excited forthe operating points considered which is most severe torsionalmode and contributes maximum negative damping. The FFTanalysis of phase “a” line current is performed in the time spanof 1–1.4 s and 2–4 s as shown in Fig. 21 and it is interesting tonote that the subsynchronous network frequency compo-nents of line current decreases with time. From the result of FFTanalysis of phase “a” of line current, it is evident that the SSCS iseffective in extracting and suppressing the subsynchronous fre-quency components of line current even when the fundamentalfrequency line current is zero. This clearly demonstrates the ef-fectiveness and robust performance of the proposed SSCS inmitigating SSR while to gain values remain unchangedunder varying operating conditions.
Fig. 16. Variation of rotor angle oscillation and LPA-LPB section torque forstep change in mechanical input torque with SSSC and subsynchronous currentsuppressor is activated at .
Fig. 17. FFT analysis of LPA-LPB section torque for case-3 (and , SSCS activated at 5 s).
C. Discussion
We propose a novel method to extract the subsynchronousfrequency components from the line current using filters. Thedesign of subsynchronous current suppressor is based on thedamping torque method [18], and genetic algorithm is adoptedfor optimizing subsynchronous current suppressor filter gains.The results demonstrate the robust performance of the systemin the entire compensation level and for the different operatingconditions.In the present work, hybrid compensation is used. While
the series active compensation is provided by the VSC basedSSSC for the enhancement of power transfer capability, theuse of subsynchronous current suppressor mitigates the SSR.The damping of all torsional modes in the entire range ofcompensation level is improved without the risk of SSR byemploying subsynchronous current suppressor.
THIRUMALAIVASAN et al.: DAMPING OF SSR USING SUBSYNCHRONOUS CURRENT SUPPRESSOR WITH SSSC 73
Fig. 18. Variation of rotor angle and LPA-LPB section torque for three-phasefault at generator terminal with SSSC and subsynchronous current suppressorwhen .
Fig. 19. Variation of rotor angle and LPA-LPB section torque for three-phasefault at generator terminal with SSSC and subsynchronous current suppressorwhen .
V. CONCLUSION
In this paper, the characteristics of a hybrid compensatedtransmission line with series capacitor and SSSC is analyzed.The converters are modeled using switching functions. Thetime invariant model is derived based on D-Q variables. Thepredictions about the stability of torsional modes using variousmethods of analysis shows good agreement. A simple techniquefor the extraction of subsynchronous frequency componentsusing filters is proposed. Filter gains are optimized using GAand is based on damping torque analysis.The following points emerge based on the results of the case
study.1) The SSSC is not strictly SSR neutral, however it offers a re-actance which remains practically constant with frequencyand increases the electrical resonant frequency of the net-work when constant reactive voltage control is adopted.
Fig. 20. Line current magnitude and D-Q components of subsynchronous cur-rent for three-phase fault at generator terminal when .
Fig. 21. FFT analysis of line current in phase “a” when .
2) The inclusion of SSSC reduces the risk of SSR by detuningthe network resonant frequency. Although the introduc-tion of SSSC reduces the peak negative damping, properlydesigned subsynchronous current suppressor improves thedamping of all the critical torsional modes.
3) The subsynchronous current suppressor effectively im-proves the damping of torsional modes in the entire rangeof compensation level and for the different operatingconditions.
4) The SSCS is effective in extracting and suppressing thesubsynchronous frequency components of line currentunder various disturbances even when the operating pointfundamental frequency line current is zero.
5) The risk of SSR is totally eliminated with the inclusion ofsubsynchronous current suppressor as electrical resonancecondition is eliminated in the practical range of series com-pensation levels.
74 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013
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R. Thirumalaivasan (M’12) received the B.E.degree from Madras University, Chennai, India, in1999 and the M.Tech degree from the College ofEngineering, Anna University, Guindy, Chennai, in2002. He is pursuing the Ph.D. degree in the Depart-ment of Electrical Engineering, JNTU Hyderabad,India.He is an Assistant Professor (Senior) in the School
of Electrical Engineering at VIT University, Vellore,India. His research interests include FACTS, HVDC,and real-time digital simulation of power electronics
and power systems.
M. Janaki (M’12) received the B.E. degree fromMadras University, Chennai, India, in 1996 andthe M.E degree from the College of Engineering,Anna University, Guindy, Chennai, in 2002. Sheis pursuing the Ph.D. degree in the Department ofElectrical Engineering, JNTU Hyderabad, India.She is an Assistant Professor (Senior) in the School
of Electrical Engineering at VIT University, Vellore,India. Her research interests include FACTS, HVDC,and power systems.
Nagesh Prabhu (M’08) received the Dipl. Elect.Engg. degree from Karnataka Polytechnic, Man-galore, India, in 1986. He graduated in ElectricalEngineering from the Institution of Engineers (India)in 1991, received the M.Tech. degree in power andenergy systems from N.I.T. Karnataka, India (for-merly Karnataka Regional Engineering College) in1995, and the Ph.D. degree from the Indian Instituteof Science, Bangalore, India, in 2005.He is presently Principal, Canara Engineering Col-
lege, Mangalore, India. He was with N.M.A.M Insti-tute of Technology, Nitte, India, from 1986 to 1998, served in J.N.N. College ofEngineering Shimoga, India, from 1998–2006 and at the VelMulti Tech Sri Ran-garajan Sakunthala Engineering College from 2006–2008 prior to joining CECMangalore. His research interests are in the area of power system dynamics andcontrol, HVDC and FACTS, and custom power controllers.Dr. Prabhu is a life member of the Indian Society for Technical Education
